From your comments, you're a bit confused about the converter and the wiring in general, I think.
The converter does not output 120VAC in any form. It only outputs 12VDC. Its output does not go through the 120VAC circuit breakers.
One of the circuit breakers does control the circuit that the converter is on, though there's a good chance there are other things on the same circuit as well. If you're really lucky, the other things will all be other items you don't want running off the inverter, like the fridge. If Mr. Murphy has his way, it'll be the outlet for the TV and DVD player. If that's the case, pianotuna has the right idea—stick a switch in the power lead to the converter. If you're feeling kind of clever, also put in a pilot light so you have a visual confirmation to check when you want to use the converter (on shore or generator power).